Toronto residents continue to drag their garbage to temporary dump sites. The strike by municipal workers began June 22. (Canadian Press)

The head of the one of the unions representing striking Toronto municipal workers has given a Sunday midnight ultimatum, saying talks will break off indefinitely with the city unless an acceptable agreement is reached.

"I am a patient man, but I am close to the end of my rope. Our bargaining committee has bent over backwards to try and meet the city’s needs," Mark Ferguson, president of CUPE Local 416, told reporters. "Many of our proposals have been rejected."

"It is time for the city to figure out how to agree to a contract that will bring the strike to a conclusion. It's time for the city to move from giving its negotiators a mandate to bargain to giving them a mandate to settle."

Municipal workers from CUPE Local 416 and CUPE Local 79 went on strike June 22. The city has been without regular services since then.

Toronto will open two new dump sites on Saturday morning. (CBC)

The strike has put 24,000 of the city's 30,000 workers on the picket line. About 6,000 workers have jobs deemed essential.

"We must have a settlement by midnight on Sunday or we are finished," Ferguson said.

Ferguson said he believes the weekend provides enough time to get a collective agreement. He said that if a deal is not reached, negotiations, from the union's perspective, will be over.

"There will be nothing else to negotiate and we will ride this labour disruption through to a conclusion."

The work stoppage has affected city-run daycares, pools, garbage collection, parks and recreation services as well as most clerical functions such as the processing of permits and public health services.

In other developments on Friday, the city said it is also opening two new temporary dump sites and closing two others.

The dump sites that will be closing at 7 p.m. on Friday are Caledonia Park and North Toronto Memorial Arena. Both have reached capacity, according to Geoff Rathbone, the city's solid waste manager.

The two new sites that will be opening are the parking lot at Amesbury Arena at 155 Culford Rd., near Lawrence Avenue West and Black Creek Drive, and the tennis courts at the Otter Creek Centre near Avenue Road and Lawrence Avenue West.

The new sites will open on Saturday at 7 a.m.